Carrollian Physics and Holography

TL;DR

This paper explores Carrollian physics and its role in flat space holography, proposing a duality between gravity in asymptotically flat spacetimes and Carrollian conformal field theories at null infinity, with connections to celestial amplitudes.

Contribution

It introduces the Carrollian limit in the context of holography, constructs Carrollian field theories, and proposes a duality linking flat space gravity to Carrollian CFTs at null infinity.

Findings

Carrollian symmetries relate to BMS symmetries in flat spacetime.

Carrollian CFTs can be derived from relativistic theories via a limiting process.

Flat space holography can be understood as a limit of AdS/CFT correspondence.

Abstract

This report reviews key developments in Carrollian physics with an emphasis on their role in the emerging framework of holography in asymptotically flat spacetimes. We begin by introducing the Carrollian limit, understood as the non-relativistic contraction of the Poincar\'e group obtained by formally taking the speed of light to zero. The geometric structures associated with this limit are described and argued to arise naturally on null hypersurfaces, most notably on null infinity, as well as black hole and cosmological horizons. Building on this, we examine the relation between the Bondi-Metzner-Sachs symmetries governing asymptotically flat gravity and the conformal Carrollian symmetries. Explicit examples of Carrollian field theories are constructed by implementing the limit on well-known relativistic field theories, with particular attention to Carrollian CFTs. We then present the Carrollian holography proposal, according to which gravity in asymptotically flat spacetimes is dual to a Carrollian CFT living at null infinity in one lower dimension. In this framework, the massless $\mathcal{S}$-matrix written in position space at null infinity is naturally reinterpreted in terms of boundary Carrollian CFT correlators, called Carrollian amplitudes. We highlight their relation to celestial amplitudes and show how they naturally emerge from holographic CFT correlators through a correspondence between the flat space limit in the bulk and the Carrollian limit at the boundary. Using this correspondence, we provide strong evidence that flat space holography arises from a controlled and consistent limiting procedure applied to both sides of the AdS/CFT duality. We conclude by outlining future directions and open questions in the program.